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Question

If f(x)=(p21p2+1)x33x+log2 is a decreasing function of x in R, then the set of possible values of p(independent of x ) is

A
(1,1)
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B
[1,)
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C
(,1]
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D
none of these
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Solution

The correct option is A (1,1)
For monotonically decreasing function f(x)<0
Therefore differentiating f(x) with respect to x
(p21p2+1)3x23<0

(p21p2+1)x2<1

Since x2>0 for all x

Therefore
(p21p2+1)<0
Or
p21<0
Or
p2<1
Or
|p|<1
Or
pϵ(1,1).

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